Problem: Solve for $x$ and $y$ using elimination. ${-x-6y = -56}$ ${x+5y = 47}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-x-6y = -56}\thinspace$ to find $x$ ${-x - 6}{(9)}{= -56}$ $-x-54 = -56$ $-x-54{+54} = -56{+54}$ $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {x+5y = 47}\thinspace$ and get the same answer for $x$ : ${x + 5}{(9)}{= 47}$ ${x = 2}$